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THEOREM 3.4. Let (X,T) be a topological space and let AX. Then the following conditions are ...
THEOREM 3.4. Let (X,T) be a topological space and let A?X. Then the following conditions are equivalent. (a) The subspace (A,TA?) is connected. (b) The set A connot be expressed as the union of two nonempty sets that are separated in X. (c) There do not exist U,V?T such that U?A?=?,V?A?=?, U?V?A=?, and A?U?V.